Method and apparatus of candidate list augmentation for channel coding system

ABSTRACT

The present invention discloses a candidate list augmentation apparatus with dynamic compensation in the coded MIMO systems. The proposed path augmentation technique in the present invention can expand the candidate paths derived from the detector to a distinct and larger list before computing the soft value of each bit. Consequently, the detector is allowed to deliver a smaller list, leading to reduction in computation complexity. Moreover, an additive correction term is introduced to dynamically compensate the approximation inaccuracy in the soft value generation, which improves the efficiency and performance of the coded MIMO systems.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates to a candidate list augmentation apparatus andmethod for channel coding system, and more particularly, a candidatelist augmentation apparatus which is able to detect signal with dynamiccompensation in the multi-input multi-output (MIMO) channel codingsystems.

2. Description of the Related Art

Multiple input multiple output (MIMO) technology draws great attentiondue to its ability to improve transmission efficiency. Among severalMIMO detection schemes, maximum likelihood (ML) detection is one of themost well known in the art which is being commonly used to fully utilizethe diversity gain. With an additive white Gaussian channel noiseassumption, ML detection can be reduced to a closest-point-searchproblem in a given lattice. Moreover, although MIMO system performanceis boosted by the diversity gain, channel coding is often employed toprovide extra coding gain such that systems are allowed to performbetter in case of lower signal-to-noise-ratio (SNR). Since exhaustivesearch is infeasible for large number of antennas or high level signalmodulation, sphere decoding has been proposed to perform exhaustivesearch after confining the search range by a radius. With properlychosen radius, sphere decoding has been proved to approach theperformance of ML detection.

Please refer to FIG. 1 for a block diagram schematically showing aconventional MIMO system 100 with channel coding schemes. Theconventional MIMO system 100 includes a channel encoder 102, a spatialmapping device 104, a transmit device 106, a receive device 108, asphere decoder 110, and a channel decoder 112. Assume that the transmitdevice 106 includes N_(t) transmit antennas and the receive device 108includes N_(r) antennas. The channel encoder 102 is utilized to channelcode the original signal u and generate the coded bits x=[x⁽¹⁾, x⁽²⁾, .. . , x^((L))]^(T). The spatial mapping device 104 then modulates thecoded bits x through L time slots. Here, Each vector x^((t))=[x₁ ^((t)),x₂ ^((t)), . . . , x_(Nt×2Mc) ^((t))] with the time index t is mapped tothe transmitted vector {tilde over (s)}⁽¹⁾=[{tilde over (s)}₁^((t)),{tilde over (s)}₂ ^((t)) . . . {tilde over (s)}_(Nt) ^((t))]^(T)by {tilde over (M)}(•), which maps 2M_(c) bits to a complex signal. Forsimplicity, the spatial mapping in the spatial mapping device 104 refersto direct spatial multiplexing, and M²-QAM-mapped signals are consideredhenceforth.

After mapping the signal, the transmit device 106 transmits through thecomplex signal based on the transmitted vector {tilde over (s)}^((t))and the receive device 108 receives the real signal according to thereceived vector {tilde over (y)}^((t)). The relation between thetransmitted vector {tilde over (s)}^((t)) and the received vector {tildeover (y)}^((t)) can be expressed by:

{tilde over (y)} ^((t)) ={tilde over (H)} ^((t)) {tilde over (s)} ^((t))+ñ ^((t))   (1)

where the channel {tilde over (H)}^((t)) is an N_(r)×N_(t) matrix ofindependent and identically distributed (i.i.d.) complex Gaussian randomvariables; ñ^((t)) is an N_(r)×1 i.i.d. complex Gaussian noise vector.The complex model in the equation (1) can be further rewritten as:

$\begin{matrix}\begin{matrix}{y^{(t)} = \begin{bmatrix}{R\left\{ {\overset{\sim}{y}}^{(t)} \right\}} \\{L\left\{ {\overset{\sim}{y}}^{(t)} \right\}}\end{bmatrix}} \\{= {{\begin{bmatrix}{{R\left\{ {\overset{\sim}{y}}^{(t)} \right\}},} & {{- L}\left\{ {\overset{\sim}{H}}^{(t)} \right\}} \\{{L\left\{ {\overset{\sim}{H}}^{(t)} \right\}},} & {R\left\{ {\overset{\sim}{y}}^{(t)} \right\}}\end{bmatrix}\begin{bmatrix}{R\left\{ {\overset{\sim}{s}}^{(t)} \right\}} \\{L\left\{ {\overset{\sim}{s}}^{(t)} \right\}}\end{bmatrix}} + \begin{bmatrix}{R\left\{ {\overset{\sim}{n}}^{(t)} \right\}} \\{L\left\{ {\overset{\sim}{n}}^{(t)} \right\}}\end{bmatrix}}} \\{= {{H^{(t)}s^{(t)}} + n^{(t)}}}\end{matrix} & (2)\end{matrix}$

where R{•} and L{•} refer to the real and the imaginary parts,respectively, of the complex signal s^((t)). Thus, the Nt-dimensionalcomplex M2-QAM signals s^((t)) are transformed into 2Nt-dimensional realM-PAM signals y^((t)). For simpler notation, the time index t will beomitted hereafter.

Based on the equation (2), ML solution can be derived by searching allover the 2N_(t)-dimensional constellation space Ω^(2Nt) for theminimizer:

$\begin{matrix}{{\hat{s}}_{ML} = {\text{arg}{\max\limits_{s^{\prime} \in \Omega^{2N_{t}}}{{y - {Hs}^{\prime}}}^{2}}}} & (3)\end{matrix}$

where the cost function ∥•∥² refers to Euclidean norm. As shown in theequation (3), the exhaustive search for the minimizer ŝ_(ML) becomesinfeasible since the computation grows exponentially with N_(t) and L.Therefore, the sphere decoder 110 in the conventional MIMO systemutilizes sphere decoding algorithm as a means to solve theclosest-lattice-point searching problem.

The sphere decoder 110 first confines the search range by a predefinedradius r; and only the path metric of the s′ in the hypersphere∥y−Hs′∥²≦r² will be compared. That is, the equation (2) can be computedby:

$\begin{matrix}{{{\hat{s}}_{ML} \approx {\hat{s}}_{SD}} = {\text{arg}{\max\limits_{{s^{\prime} \in \Omega^{2N_{t}}},{{{y - {Hs}^{\prime}}}^{2} \leq r^{2}}}{{y - {Hs}^{\prime}}}^{2}}}} & (4)\end{matrix}$

Here, if the radius r is chosen properly such that at least one path s′satisfies the radius constraint.

Next, the sphere decoder 110 will preprocess on y to transform theequation (4) into a tree-search problem. By QR-decomposition, forinstance, the channel matrix is decomposed by H=QR where Q^(T)Q=I_(2Nr),an identity matrix of size 2N_(r), and R is a 2N_(t)×2N_(t) uppertriangular matrix. By multiplying y with Q^(T), the sphere decoder 110can transformed the equation (4) into:

$\begin{matrix}{{\hat{s}}_{ML} = {\text{arg}{\min\limits_{s^{\prime} \in \Omega^{2N_{t}}}{{q - {Rs}^{\prime}}}^{2}}}} & (5)\end{matrix}$

where q=[q₁, q₂, . . . , q_(2Nt)]=Q^(T)y. Each s′ in Ω^(2Nt) is definedas a “path” that traverses from the root to the leaf of the search tree.Every path consists of 2N_(t) nodes representing the 2N_(t) points ofthe 2N_(t)-layered tree. Moreover, the cost function of each path, i.e.∥q−Rs′∥², will be referred to “path metric” and can be calculated by:

$\begin{matrix}{{{q - {Rs}^{\prime}}}^{2} = {{\sum\limits_{i = 1}^{2{Nt}}\left( {q_{i} - {\sum\limits_{j = i}^{2{Nt}}{R_{i,j}s_{j}}}} \right)^{2}} = {\sum\limits_{i = 1}^{2{Nt}}{e\left( s^{(i)} \right)}}}} & (6)\end{matrix}$

where s^((i)) represents the i-th to 2Nt-th elements of s′, that is,s^((i))=[s_(i), s_(i+1), . . . , s_(2Nt)]^(T). Moreover, the partialEuclidean distance (PED) of s^((i)), T(s^((i))), is defined by:

$\begin{matrix}{{T\left( s^{(i)} \right)} = {{\sum\limits_{i = 1}^{2{Nt}}\left( {q_{i^{\prime}} - {\sum\limits_{j = i^{\prime}}^{2{Nt}}{R_{i^{\prime},j}s_{j}}}} \right)^{2}} = {{T\left( s^{({i + 1})} \right)} + {e\left( s^{(i)} \right)}}}} & (7)\end{matrix}$

Based on this conventional sphere decoding algorithm, the minimizerŝ_(ML) can be found as long as each path has been searched. However, thetraditional sphere decoding algorithm remains a major challenge inacquiring accurate probabilistic information. Limited by the complexcomputation of sphere decoding, and inconstant decoding throughput couldcause inefficient VLSI implementation.

Different from the sphere decoding algorithm that outputs only the MLpath, the conventional MIMO system utilizes the modified list spheredecoding algorithm to deliver a candidate list L that consists of themost reliable paths. Please refer to FIG. 2 for a block diagramschematically showing another conventional MIMO system 200 with listsphere coding schemes. The conventional MIMO system 200 includes achannel encoder 202, a spatial mapping device 204, a transmit device206, a receive device 208, a list sphere decoder 210, and a channeldecoder 216. Since the elements of the same name in the FIG. 1 and FIG.2 have the same function and operation, detailed description is omittedfor the sake of brevity. The main different between the MIMO systems 100and 200 is that the MIMO systems 200 further includes the list spheredecoder 210. The list sphere decoder 210 includes a candidate listgeneration device 212 and a soft value generation device 214. Thecandidate list generation device 212 is utilized to generate a candidatelist L. Assume that |L| is the list size. Based on the system model inthe equation (2), the most reliable |L| paths are equivalent to thepaths corresponding to the least |L| path metrics. After generating thecandidate list L, the soft value generation device 214 then computes thesoft input signal from the list L for the subsequent channel decoder216. Different soft input signal can result in different errorcorrecting capability for the following channel decoding. The operationof the candidate list generation device 212 and the soft valuegeneration device 214 are further detailed as follows.

Let M(•) denote the M-PAM mapping function such that s_(k)=M(x_(k,1),x_(k,2), . . . , x_(k,Mc)). For any path s′ε L, the soft value ofx_(k,j) is defined by its “a posteriori” probabilities:

$\begin{matrix}\begin{matrix}{{L\left( x_{k,j} \right)} = {\log \frac{\Pr \left( {x_{k,j} = \left. 0 \middle| y \right.} \right)}{\Pr \left( {x_{k,j} = \left. 1 \middle| y \right.} \right)}}} \\{= {{\log \frac{\Pr \left( {x_{k,j} = 0} \right)}{\Pr \left( {x_{k,j} = 1} \right)}} + {\log \frac{\Pr \left( {\left. y \middle| x_{k,j} \right. = 0} \right)}{\Pr \left( {\left. y \middle| x_{k,j} \right. = 1} \right)}}}}\end{matrix} & \begin{matrix}(8) \\\; \\(9)\end{matrix}\end{matrix}$

The first term in the equation (9), which is the “a priori” information,is zero for the ML detection or can be computed by the extrinsicinformation provided by the channel decoder in an iterative detectiondecoding process. The second term in the equation (9) can be computedby:

$\begin{matrix}{{\log \frac{\Pr \left( {\left. y \middle| x_{k,j} \right. = 0} \right)}{\Pr \left( {\left. y \middle| x_{k,j} \right. = 1} \right)}} = {\log \frac{\sum\limits_{s^{\prime} \in \Omega_{j,0}}{\Pr \left( y \middle| s^{\prime} \right)}}{\sum\limits_{s^{\prime} \in \Omega_{j,1}}{\Pr \left( y \middle| s^{\prime} \right)}}}} & (10) \\{\approx {\frac{1}{2\sigma^{2}}\left( {{\min\limits_{s^{\prime} \in \Omega_{j,1}}{{y - {Hs}^{\prime}}}^{2}} - {\min\limits_{s^{\prime} \in \Omega_{j,0}}{{y - {Hs}^{\prime}}}^{2}}} \right)}} & (11) \\{\approx {\frac{1}{2\sigma^{2}}\left( {{\min\limits_{s^{\prime} \in {\Omega_{j,1}\bigcap L}}{{y - {Hs}^{\prime}}}^{2}} - {\min\limits_{s^{\prime} \in {\Omega_{j,0}\bigcap L}}{{y - {Hs}^{\prime}}}^{2}}} \right)}} & (12)\end{matrix}$

Where σ² is the noise variance, and Ω_(j,b) is the set of all path s′having x_(k,j)=b for b=0, 1. That is, Ω_(j,0) represents the set of alls′ having x_(k,j)=0, and Ω_(j,0) represents the set of all s′ havingx_(k,j)=1. Usually, the candidate list generation device 212 willgenerate a sufficiently large list to ensure a high probability infinding the true minimizer in the equation (11) with (12). Withpreprocessing, the equation (12) will be replaced by:

$\begin{matrix}{\frac{1}{2\sigma^{2}}\left( {{\min\limits_{s^{\prime} \in {\Omega_{j,1}\bigcap L}}{{q - {Rs}^{\prime}}}^{2}} - {\min\limits_{s^{\prime} \in {\Omega_{j,0}\bigcap L}}{{q - {Rs}^{\prime}}}^{2}}} \right)} & (13)\end{matrix}$

However, when one of the sets Ω_(j,0) and Ω_(j,0) can not find the paths′ in the list L (i.e. Ω_(j,0)∩L=0 or Ω_(j,1)∩L=0), it is impossible tofind the minimizer in an empty set, and the minima is often approximatedby a predefined large constant. Being the soft input signals to thesubsequent channel decoder 216, the additional interference resultedfrom the approximation inaccuracy can degrade the error performance.Although the degradation can be mitigated by increasing the list size toreduce the probability of Ω_(j,0)∩L (or Ω_(j,1)∩L), being an empty set,the computation complexity in generating the candidate list alsoincreases.

Therefore, to solve the above-mentioned problems, the present inventionproposes a novel candidate list augmentation apparatus for channelcoding system and method thereof along with dynamic compensation toimprove the efficiency and performance of the coded MIMO systems.

SUMMARY OF THE INVENTION

It is therefore one of the many objectives of the claimed invention toprovide candidate list augmentation apparatus and method thereof alongwith dynamic compensation to improve the efficiency and performance ofthe coded MIMO systems.

According to the claimed invention, a candidate list augmentation deviceis disclosed. The candidate list augmentation device includes acandidate list generation device for receiving an input signal within acoded MIMO system and generating a candidate list according to saidinput signal; a path augmentation device, coupled to said candidate listgeneration device, for augmenting paths in the candidate list accordingto said candidate list and generate an augmented list; and a soft valuegeneration device, coupled to said candidate list generation device andsaid path augmentation device, for comparing said input signal and saidaugmented list and generating a soft value according to said inputsignal, said candidate list and said augmented list, wherein said softvalue is utilized for error correcting in decoding said input signal.

Also according to the claimed invention, a candidate list augmentationmethod with low-complexity soft value generation for the coded MIMOsystems is disclosed. The candidate list augmentation method includes(1) receiving an input signal and generating a candidate list accordingto said input signal; (2) generating an augmented list according to saidcandidate list; and (3) comparing said input signal and said augmentedlist and generating a soft value according to said input signal, saidcandidate list and said augmented list, wherein said soft value isutilized for error correcting in decoding said input signal.

Below, the embodiments of the present invention are described in detailin cooperation with the attached drawings to make easily understood theobjectives, technical contents, characteristics and accomplishments ofthe present invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram schematically showing a conventional MIMOsystem with channel coding schemes;

FIG. 2 is a block diagram schematically showing another conventionalMIMO system with list sphere coding schemes;

FIG. 3 is a block diagram schematically showing a MIMO system withcandidate list augmentation scheme according to the present invention;

FIG. 4 is diagram schematically showing an example of the operation ofthe path augmentation device according to the present invention; and

FIG. 5 is a diagram schematically showing a simulation result accordingto the present invention.

DETAILED DESCRIPTION OF THE INVENTION

The present invention provides a candidate list augmentation device andmethod thereof for channel coding systems with dynamic compensation toimprove the efficiency and performance of the channel coding systemespecially coded MIMO systems

Please refer to FIG. 3 for a block diagram schematically showing a MIMOsystem 300 with candidate list augmentation scheme according to thepresent invention. The MIMO system 300 includes a channel encoder 302, aspatial mapping device 304, a transmit device 306, a receive device 308,a list sphere decoder 310, and a channel decoder 318. The list spheredecoder 310 includes a candidate list generation device 312, a softvalue generation device 314, and a path augmentation device 316. Thecandidate list generation device 312 is mainly responsible for receivingan input signal within the coded MIMO system and generating a candidatelist according to this input signal. As for the path augmentation device316 which is coupled to the candidate list generation device 312, it isresponsible for augmenting paths in the candidate list according to thecandidate list and then generate an augmented list. The soft valuegeneration device 314 which is coupled to the candidate list generationdevice 312 and the path augmentation device 316 provides comparison forthe input signal and the augmented list, and then generates a soft valueaccording to the input signal, the candidate list and the augmentedlist, wherein said soft value is utilized for error correcting indecoding the input signal. Since the elements of the same name in theFIG. 2 and FIG. 3 have the same function and operation, detaileddescription is omitted for the sake of brevity. In the presentinvention, the path augmentation device 316 is applied to equivalentlyprovide a larger candidate list, and the probability of failing to findthe minimizer in the augmented list is reduced accordingly. That is, thepath augmentation device 316 can be treated as an enhancement; nomodifications are required for the candidate list generation device 312and the soft value generation device 314 based on the conventionalschemes.

For the soft value L(x_(k,j)) computation, the path augmentation device316 will expand each path s′ in L to M paths by first duplicating s′ M−1times. Next, each the k-th element of the M identical paths is replacedby a distinct ω_(j) from Ω={ω_(j)|j=0, 1, . . . ,M−1}, the M symbols ofM-PAM constellation. This duplicating-and-replacing procedure continuesuntil all the paths in L are examined. As a result, L is expended toL_(k) and |L_(k)|=M×|L|. Although identical paths may be found in L_(k),Ω_(j,0)∩L_(k) or Ω_(j,1)∩L_(k) will never be empty sets since theaugmented list contains all constellation points at the k-th layer.Besides, the paths in L are believed to be more reliable, and theaugmented list is supposed to be reliable as well. It can be inferredthat:

$\begin{matrix}{{{\min\limits_{s^{\prime} \in \Omega_{j,0}}{{y - {Hs}^{\prime}}}^{2}} \approx {\min\limits_{s^{\prime} \in {\Omega_{j,0}\bigcap L_{K}}}{{y - {Hs}^{\prime}}}^{2}}}{And}} & (14) \\{{\min\limits_{s^{\prime} \in \Omega_{j,1}}{{y - {Hs}^{\prime}}}^{2}} \approx {\min\limits_{s^{\prime} \in {\Omega_{j,1}\bigcap L_{K}}}{{y - {Hs}^{\prime}}}^{2}}} & (15)\end{matrix}$

Moreover, the path metric of the j-th expanded path from s′ can becomputed by

T(s′)+(Δ_(i) R _(i,i))²+2(y _(i) −Σ _(j=i) ^(2N) ^(t) R _(i,j) S _(j))R_(i,i)Δ_(i)   (16)

where Δ_(j)=s_(k)−ω_(j) for j=0, 1, . . . , M−1.

For example, please refer to FIG. 4 for a diagram schematically showingan example of the operation of the path augmentation device 316according to the present invention. Assume that the path augmentationdevice 316 is used for computing L(x_(5,0)) and L(x_(5,1)) in a 16-QAM4×4 MIMO system. The equivalent 4-PAM 8-layered tree can be representedby an 8-stage trellis diagram. Each path s′ in L corresponds to a pathin the trellis. In this example, s′={+1,−1,−1,+1,+3,−1,−3,−1}, M=4, andΩ={−3,−1,+1,+3}. The path augmentation device 316 can expand the path s′to the four distinct path that contains all constellation points of s₅for computing L(x_(5,0)) and L(x_(5,1)) by the duplicating-and-replacingprocedure. As shown in FIG. 4, the solid lines are for Ω_(j,0) and thedashed lines are for Ω_(j,1).

The above-mentioned procedure needs to be performed 2N_(t) times fordecoding s, and the equation (16) is the major computation overhead.Note that Δ_(j) have limited values and ranges, and they can be realizedby a simple look up table or a decoder. Please note that, in thisembodiment, the path s′ can be expanded to unlimited M paths. However,considering the overhead from the path augmentation device 316, L_(k)can also be augmented partially. That is, the soft values can begenerated by the |L|×M most reliable paths for 0<M<1. The value M canprovide a tradeoff between complexity and error performance.

Moreover, the path augmentation device 316 in the present invention canfurther perform the dynamic compensation by introducing an additivecorrection term to improve the approximation accuracy of the channeldecoder 318 and to improve the error performance. Here, let n₀ and n₁denote the sizes of Ω_(j,0)∩L_(k) and Ω_(j,1)∩L_(k) respectively, andn₀+n₁=|L|. Moreover, let

$\begin{matrix}{{m_{0} = {\min\limits_{s^{\prime} \in \Omega_{j,0}}{{q - {Rs}^{\prime}}}^{2}}}{And}} & (17) \\{m_{1} = {\min\limits_{s^{\prime} \in \Omega_{j,1}}{{q - {Rs}^{\prime}}}^{2}}} & (18)\end{matrix}$

And the path augmentation device 316 can express the equation (10) inthe conventional list sphere decoding algorithm as follows:

$\begin{matrix}\begin{matrix}{{\log \frac{\sum\limits_{s^{\prime} \in \Omega_{j,0}}{\Pr \left( y \middle| s^{\prime} \right)}}{\sum\limits_{s^{\prime} \in \Omega_{j,1}}{\Pr \left( y \middle| s^{\prime} \right)}}} = {\log \frac{\sum\limits_{s^{\prime} \in \Omega_{j,0}}{\Pr \left( q \middle| s^{\prime} \right)}}{\sum\limits_{s^{\prime} \in \Omega_{j,1}}{\Pr \left( q \middle| s^{\prime} \right)}}}} \\{= {\frac{\left( {m_{1} - m_{0}} \right)}{2\sigma^{2}} + {\log \frac{1 + {\sum\limits_{i = 1}^{n_{0} - 1}^{\frac{- 1}{2\sigma^{2}}{({a_{i} - m_{0}})}}}}{1 + {\sum\limits_{i = 1}^{n_{1} - 1}^{\frac{- 1}{2\sigma^{2}}{({b_{i} - m_{1}})}}}}}}}\end{matrix} & (19)\end{matrix}$

where {m₀, a₁, a₂, . . . , a_(n0−1)}={T(s′)}|∀s′εΩ_(j,0)∩L}, and {m₁,b₁, b₂, . . . , b_(n1−1)}={T(s′)}|∀s′εΩ_(j,1)∩L}. For sufficiently largelist size,

${{\log \; \frac{n_{0}}{n_{1}}} \approx \frac{\Pr \left( {x_{j} = 0} \right)}{\Pr \left( {x_{j} = 1} \right)}},$

which is the intrinsic information required by an maximum “a posteriori”(MAP) detector.The second term in (19) and the intrinsic information can be combined as

$\begin{matrix}{{\beta \; \log \frac{1 + n_{0}}{1 + n_{1}}} \cong {{\log \frac{\left( {1 + {\sum\limits_{i = 1}^{n_{0} - 1}^{\frac{1}{2\sigma^{2}}{({a_{i} - m_{0}})}}}} \right)}{\left( {1 + {\sum\limits_{i = 1}^{n_{1} - 1}^{\frac{- 1}{2\sigma^{2}}{({b_{i} - m_{1}})}}}} \right)}} + {\log \frac{\Pr \left( {x_{j} = 0} \right)}{\Pr \left( {x_{j} = 1} \right)}}}} & (20)\end{matrix}$

where

$\frac{n_{0}}{n_{1}}$

is modified to

$\frac{1 + n_{0}}{1 + n_{1}}$

to avoid logarithm of zero or infinity. Ultimately, the soft valuegenerated by the soft value generation device 314 will be:

$\begin{matrix}{{L\left( x_{k,j} \right)} \approx {\frac{- 1}{2\sigma^{2}}\left( {m_{1} - m_{0} + {\beta \; \log \frac{1 + n_{0}}{1 + n_{1}}}} \right)}} & (21) \\{\mspace{65mu} {\approx \left( {m_{1} - m_{0} + {{\beta log}\frac{1 + n_{0}}{1 + n_{1}}}} \right)}} & (22)\end{matrix}$

where β is a normalization factor, and n₁=|L|−n₀. From the equation(21), the computation overhead resulted from the dynamic compensation

$\beta \; \log \frac{1 + n_{0}}{1 + n_{1}}$

are one multiplication, two logarithms, and at most |L|+1 additions foraccumulating n₀. Moreover, m₀ (or m₁) will be estimated by the maximumpath metric in L if Ω_(j,0)∩L_(k) (or Ω_(j,1)∩L_(k)) is empty set.Please note that, in this embodiment, the calculation of the soft valueL(x_(k,j)) in the equation (21) and (22) is the estimated value suitablefor current model. However, the calculation of the soft value L(x_(k,j))is not limited to the above definition. That is, in other embodiments,the soft value L(x_(k,j)) can be assigned by different conditionsdepending on design requirements. For example, for simplicity, the softvalue generation device 314 can alternatively generate the soft valueL(x_(k,j)) by:

L(x _(k,j))≈m ₁ −m ₂   (23)

Please refer to FIG. 5 for a diagram schematically showing a simulationresult according to the present invention. The simulation is based on a4×4 MIMO system wherein (648,324) and (1944, 972) LDPC codes ofIEEE802.11n is applied as channel coding schemes. The candidate listgeneration is realized by the K-best algorithm. To achieve the BER lowerthan 10⁻⁵, FIG. 5 shows that the conventional LSDs should have the listsize K larger than 128. However, as shown in FIG. 5, the proposedcandidate list augmentation scheme (A-LSD) in the present invention canachieve SNR improvement from 0.3 dB to 1 dB, depending on K value, andthe improvement becomes more apparent when K value is smaller. That is,the path augmentation algorism in the present invention results inequivalently more available candidates, and therefore 64-best A-LSD hasthe lowest error floor.

Based on the present invention, the path augmentation algorithm in thepresent invention guarantees a low probability of failing to find theminimizers. Actually, the computation overhead from list expansion bythe path augmentation device 316 is usually smaller as compared todirect generation of a larger candidate list in the conventional MIMOsystem. Moreover, the path augmentation algorithm in the presentinvention can be applied in different decoding algorithm, for instance,sphere decoding, list decoding, M-algorithm, T-algorithm, or K-bestalgorithm. Besides, an additive correction term is introduced todynamically compensate the approximation loss in the conventional listsphere decoding scheme. Combining the two proposed schemes, the MIMOsystem with candidate list augmentation scheme in the present inventionsignificantly reduce the calculation complex and perceive improvement inerror performance.

Those described above are only the preferred embodiments to exemplifythe present invention but not to limit the scope of the presentinvention. Any equivalent modification or variation according to theshapes, structures, features and spirit disclosed in the specificationis to be also included within the scope of the present invention.

1. A candidate list augmentation device for channel coding systems, saiddevice comprising: a candidate list generation device for receiving aninput signal within a channel coding system and generating a candidatelist according to said input signal; a path augmentation device, coupledto said candidate list generation device, for augmenting paths in thecandidate list according to said candidate list and generate anaugmented list; and a soft value generation device, coupled to saidcandidate list generation device and said path augmentation device, forcomparing said input signal and said augmented list and generating asoft value according to said input signal, said candidate list and saidaugmented list, wherein said soft value is utilized for error correctingin decoding said input signal.
 2. The candidate list augmentation deviceof claim 1, wherein said candidate list comprises a plurality of paths,and each said path comprises a plurality of bit information for decodingsaid input signal.
 3. The candidate list augmentation device of claim 1,wherein said candidate list generation device can generate saidcandidate list by the sphere decoding algorithm, the list decodingalgorithm, M-algorithm, T-algorithm, or K-best algorithm.
 4. Thecandidate list augmentation device of claim 1, wherein said channelcoding system includes coded MIMO system.
 5. The candidate listaugmentation device of claim 1, wherein said path augmentation devicegenerates said augmented list by expanding each said path in saidcandidate list to M paths by duplicating each said path M−1 times; andreplacing said k-th bit information in said M paths by a distinct ω_(j)from a original set Ω={ω_(j)|j=0, 1, . . . , M−1}.
 6. The candidate listaugmentation device of claim 5, wherein said path augmentation devicecould separate said M paths in said candidate list into a first setΩ_(j,0) and a second set Ω_(j,1), wherein said first set Ω_(j,0) denotesj-th bit information of said paths in said first set is in a first digit(zero), and Ω_(j,1) denotes j-th bit information of said paths in saidsecond set is in a second digit (one).
 7. The candidate listaugmentation device of claim 6, wherein said path augmentation devicecan calculate a first minimizer m₀ for said first set Ω_(j,0) by${m_{0} = {\min\limits_{s^{\prime} \in \Omega_{j,0}}{{q - {Rs}^{\prime}}}^{2}}},$and a second minimizer m₁ for said second set Ω_(j,0) by${m_{1} = {\min\limits_{s^{\prime} \in \Omega_{j,1}}{{q - {Rs}^{\prime}}}^{2}}},{{wherein}\mspace{14mu} {{q - {Rs}^{\prime}}}^{2}}$refers to the path metric of said candidate list.
 8. The candidate listaugmentation device of claim 7, wherein said soft value generationdevice generated said soft value L(x_(k,j)) by the following equation:${L\left( x_{k,j} \right)} \approx {\frac{- 1}{2\sigma^{2}}\left( {m_{1} - m_{0} + {\beta \; \log \frac{1 + n_{0}}{1 + n_{1}}}} \right)}$wherein σ² is the noise variance, β is a normalization factor, n₀ and n₁denote the sizes of Ω_(j,0) and Ω_(j,1) respectively, and n₀+n₁ areequal to the size of said candidate list.
 9. The candidate listaugmentation device of claim 7, wherein said soft value generationdevice generated said soft value L(x_(k,j)) by the following equation:${L\left( x_{k,j} \right)} \approx {m_{1} - m_{0} + {\beta \; {\log\left( \frac{1 + n_{0}}{1 + n_{1}} \right)}}}$wherein β is a normalization factor, n₀ and n₁ denote the sizes ofΩ_(j,0) and Ω_(j,1) respectively, and n₀+n₁ are equal to the size ofsaid candidate list.
 10. The candidate list augmentation device of claim7, wherein said soft value generation device generated said soft valueL(x_(k,j)) by the following equation: L(x_(k,j))≈m₁−m₀.
 11. An candidatelist augmentation method for channel coding systems, said methodcomprising: (1) receiving an input signal and generating a candidatelist according to said input signal; (2) generating an augmented listaccording to said candidate list; and (3) comparing said input signaland said augmented list and generating a soft value according to saidinput signal, said candidate list and said augmented list, wherein saidsoft value is utilized for error correcting in decoding said inputsignal.
 12. The candidate list augmentation method of claim 11, whereinsaid candidate list comprises a plurality of paths, and each said pathcomprises a plurality of bit information for decoding said input signal.13. The candidate list augmentation method of claim 11, wherein saidstep (1) further comprises: generating said candidate list by the spheredecoding algorithm, the list decoding algorithm, M-algorithm,T-algorithm, or K-best algorithm.
 14. The candidate list augmentationmethod of claim 11, wherein said step (2) further comprises: expandingeach said path in said candidate list to M paths by duplicating eachsaid path M−1 times; and replacing said k-th bit information in said Mpaths by a distinct ω_(j) from a original set Ω={ω_(j)|j=0, 1, . . .,M−1} in said candidate list.
 15. The candidate list augmentation methodof claim 14, wherein said step (2) further comprises: separating said Mpaths in said candidate list into a first set Ω_(j,0) and a second setΩ_(j,1), wherein said first set Ω_(j,0) denotes j-th bit information ofsaid paths in said first set is in a first digit (zero), and Ω_(j,1)denotes j-th bit information of said paths in said second set is in asecond digit (one).
 16. The candidate list augmentation method of claim15, wherein a first minimizer m₀ can be calculated for said first setΩ_(j,0) by${m_{0} = {\min\limits_{s^{\prime} \in \Omega_{j,0}}{{q - {Rs}^{\prime}}}^{2}}},$and a second minimizer m₁ can be calculated for said second set Ω_(j,0)by${m_{1} = {\min\limits_{s^{\prime} \in \Omega_{j,1}}{{q - {Rs}^{\prime}}}^{2}}},$wherein ∥q−Rs′∥² refers to the path metric of said candidate list. 17.The candidate list augmentation method of claim 16, wherein said softvalue L(x_(k,j)) can be generated by the following equation:${L\left( x_{k,j} \right)} \approx {\frac{- 1}{2\sigma^{2}}\left( {m_{1} - m_{0} + {\beta \; \log \frac{1 + n_{0}}{1 + n_{1}}}} \right)}$wherein σ² is the noise variance, β is a normalization factor, n₀ and n₁denote the sizes of Ω_(j,0) and Ω_(j,1) respectively, and n₀+n₁ areequal to the size of said candidate list.
 18. The candidate listaugmentation method of claim 16, wherein said said soft value L(x_(k,j))can be generated by the following equation:${L\left( x_{k,j} \right)} \approx {m_{1} - m_{0} + {\beta \; {\log\left( \frac{1 + n_{0}}{1 + n_{1}} \right)}}}$wherein β is a normalization factor, n₀ and n₁ denote the sizes ofΩ_(j,0) and Ω_(j,1) respectively, and n₀+n₁ are equal to the size ofsaid candidate list.
 19. The candidate list augmentation method of claim16, wherein said said soft value L(x_(k,j)) can be generated by thefollowing equation: L(x_(k,j))≈m₁−m₀.